TIME AND WORK

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1. A is able to do a piece of work in 15 days and B can do the same work in 20 days. If they can work together for 4 days, what is the fraction of work left?

Ans- 8/15

 EXPLANATION – 

Amount of work A can do in 1 day = 1/15

Amount of work B can do in 1 day = 1/20

Amount of work A and B can do in 1 day = 1/15 + 1/20 = 7/60

Amount of work A and B can together do in 4 days = 4 × (7/60) = 7/15

Fraction of work left = 1 – 7/15= 8/15

Q  2- P is thrice as good as Q in work. P is able to finish a job in 60 days less than Q. They can finish the work in – days if they work together.

ANS-  22 ½ days

EXPLANANTION

If P  completes a work in 1 day, Q completes the same work in 3 days

Hence, if the difference is 2 days, Q can complete the work in 3 days

=> if the difference is 60 days, Q can complete the work in 90 days

=> Amount of work Q  can do in 1 day= 1/90

Amount of work P can do in 1 day = 3 × (1/90) = 1/30

Amount of work P and Q can together do in 1 day = 1/90 + 1/30 = 4/90 = 2/45

=> P and Q together can do the work in 45/2 days = 22 ½ days

Q 3-  6 men and 8 women can complete a work in 10 days. 26 men and 48 women can finish the same work in 2 days. 15 men and 20 women can do the same work in – days.

ANS- 4 days

EXPLANANTION

Let work done by 1 man in 1 day = m and work done by 1 woman in 1 day = b

Work done by 6 men and 8 women in 1 day = 1/10

=> 6m + 8b = 1/10

=> 60m + 80b = 1 — (1)

Work done by 26 men and 48 women in 1 day = 1/2

=> 26m + 48b = ½

=> 52m + 96b = 1— (2)

Solving equation 1 and equation 2. We get m = 1/100 and b = 1/200

Work done by 15 men and 20 women in 1 day

= 15/100 + 20/200 =1/4

=> Time taken by 15 men and 20 women in doing the work = 4 days

Q6-  A can do a work in the same time in which B and C together can do it. If A and B work together, the work can be completed in 10 days. C  alone needs 50 days to complete the same work. then B alone can do it in

ANS- 25 DAYS

EXPLANANTION

Work done by A and B in 1 day = 1/10

Work done by C in 1 day = 1/50

Work done by A, B and C in 1 day = 1/10 + 1/50 = 6/50

But Work done by A in 1 day = Work done by B and C in 1 day . Hence the above equation can be written as

Work done by A in 1 day × 2 = 6/50

=> Work done by A in 1 day = 3/50

=> Work done by B and C in 1 day = 3/50

Hence work done by B in 1 day = 3/50 – 1/50 = 2/50 = 1/25

So B alone can do the work in 25 days